2. If yes, when would be a good time to start studying a supplementary martial art?

In my opinion, the biggest problem beginners run into is setting aside what they have learned before and clearly seeing and then trying what they are now being presented with. Again, just my opinion, but I feel that we should dive into the martial art we have chosen, as deeply as possible, for at least five years (should be longer) before we look into another martial art.

I have read that Masaaki Hatsumi has said that it takes the guy who has done five years of Judo, five years to get all of the Judo out of his system to start at zero, in year six, to learn the new art. I think this is a bit of an exaggeration, but there is a lot of wisdom in the statement.